Consider any acute angle

MATHEMATICS · Subjective · CBSE · Mathematics · Introduction to Trigonometry · Introduction to Trigonometry

Problem

Consider any acute angle θ\theta. (a) Expand and simplify the product (1+sin⁡θ)(1−sin⁡θ)(1+\sin\theta)(1-\sin\theta). (b) Show that the simplified result obtained in part (a) is equal to cos⁡2θ\cos^{2}\theta. (c) Hence simplify the fraction 1−sin⁡2θcos⁡2θ\dfrac{1-\sin^{2}\theta}{\cos^{2}\theta} and state its value. (d) If sin⁡θ=1213\sin\theta = \dfrac{12}{13}, determine tan⁡θ\tan\theta and confirm that your answer is consistent with the result of part (b).

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